Question

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Answer 1

Volume : 4186.66 cm^3.

_____✌_____

Answer 2

Answer:

$\large{\underline{\underline{\textsf{\textbf{Diagram : -}}}}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bf 10\ cm}\end{picture}$

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\textsf{\textbf{Given : -}}}}}$

• ↠ Surface area of sphere = 1256 cm².

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\textsf{\textbf{To Find : -}}}}}$

• ↠ Volume of sphere

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\textsf{\textbf{Using Formulas : -}}}}}$

$\small{\bigstar{\underline{\boxed{\sf{\pink{Surface \: area \: of \: sphere = 4\pi{r}^{2}}}}}}}$

$\small{\bigstar{\underline{\boxed{\sf{\pink{Volume \: of \: sphere = \dfrac{4}{3}\pi{r}^{3}}}}}}}$

$\small\bigstar$ Where :-

• ↠ π = 3.14
• ↠ r = radius

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\textsf{\textbf{Solution : -}}}}}$

$\small\bigstar$ Firstly, finding the radius of sphere by substituting the values in the formula :-

$\small{\dashrightarrow{\sf{Surface \: area \: of \: sphere = 4\pi{r}^{2}}}}$

$\small{\dashrightarrow{\sf{1256 = 4 \times 3.14\times {r}^{2}}}}$

$\small{\dashrightarrow{\sf{1256= 12.56\times {r}^{2}}}}$

$\small{\dashrightarrow{\sf{{(Radius)}^{2} = \dfrac{1256}{12.56}}}}$

$\small{\dashrightarrow{\sf{{(Radius)}^{2} = \dfrac{1256 \times 100}{12.56 \times 100}}}}$

$\small{\dashrightarrow{\sf{{(Radius)}^{2} = \dfrac{125600}{1256}}}}$

$\small{\dashrightarrow{\sf{{(Radius)}^{2} = \cancel{\dfrac{125600}{1256}}}}}$

$\small{\dashrightarrow{\sf{{(Radius)}^{2} =100}}}$

$\small{\dashrightarrow{\sf{Radius = \sqrt{100} }}}$

$\small{\dashrightarrow{\sf{Radius = \sqrt{ 10\times 10}}}}$

$\small{\dashrightarrow{\underline{\underline{\sf{Radius=10 \: cm}}}}}$

$\normalsize{\bigstar{\underline{\boxed{\sf{\purple{Radius \: of \: sphere =10 \: cm}}}}}}$

Hence, the radius of sphere is 10 cm.

$\begin{gathered}\end{gathered}$

$\small\bigstar$ Now, finding the volume of sphere by substituting the values in the formula :-

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{4}{3}\pi{r}^{3}}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{4}{3} \times 3.14 \times {(10)}^{3}}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{4 \times 3.14}{3} \times (10 \times 10 \times 10)}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{12.56}{3} \times 1000}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{12.56 \times 1000}{3}}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \dfrac{12560}{3}}}}$

$\small{\dashrightarrow{\sf{Volume \: of \: sphere = \cancel{\dfrac{12560}{3}}}}}$

$\small{\dashrightarrow{\underline{\underline{\sf{Volume \: of \: sphere \approx 4186.66 \: {cm}^{3}}}}}}$

$\normalsize{\bigstar{\underline{\boxed{\sf {\purple{Volume \: of \: sphere \approx 4186.66 \: {cm}^{3}}}}}}}$

Hence, the volume of sphere is 4186.66 cm³.

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\textsf{\textbf{Learn More : -}}}}}$

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

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